Apply the distributive property to
create an equivalent expression.
(-7c + 8d)0.6

Answer:

  124.2 miles

  ∠310.1°

Step-by-step explanation:

You want to know the bearing and distance to the airport from a plane that is 95 miles east and 80 miles south of it.

The Pythagorean theorem or the distance formula can be used to find the distance to the airport.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((95 -0)² +(-80 -0)²) = √(9025 +6400) = √15425

  d ≈ 124.197 . . . . miles

The plane is about 124.2 miles from the airport.

The reference angle with respect to the +y axis can be found using the tangent relation.

  Tan = Opposite/Adjacent

  tan(α) = 95/80 = 19/16

  α = arctan(19/16) ≈ 49.9° . . . . . . CCW from +y axis

The bearing angle is measured clockwise from the +y axis (north), so is ...

  bearing = 360° -49.9° = 310.1°

The bearing to the airport is 310.1°.

__

Additional comment

Some navigators would refer to the bearing as N 49.9° W.

Less commonly, it might be referred to as W 40.1° N. Usually, N and S are the reference directions, with the modification being E or W from there. The less common usage might be chosen if an angle less than 45° is wanted.

The bearing is often reported to the nearest degree, without any degree symbol, as N50W.

The equation of the absolute value function graph is: y = |x - 3| + 5.

The equation, y = a|x – h| + k, represents the equation of an absolute value function in the vertex form, where:

We are given the following from the graph:

Vertex (h, k) = (3, 5)

Plug in the values of h and k into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (5, 7). Find the value of a by substituting (x, y) = (5, 7) into y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = a|2| + 5

7 = 2a + 5

7 - 5 = 2a

2 = 2a

2/2 = 2a/2

1 = a

a = 1

Write the equation of the absolute function graph by substituting a = 1 into y = a|x - 3| + 5:

y = |x - 3| + 5

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11.5 and 15 are the values that are part of the solution set of the inequality.

Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

-4x + 24 < -2x + 2

-4x + 2x < -24 + 2

-2x < -22

22 < 2x

11 < x

Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.

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y = 0.1x + 1 is the linear function for pressure based on the depth in meters

Given that:  At 30 meters in depth the water pressure measures 4 (atm)

At 50 meters in depth under water the pressure is 6 (atm)

We will consider the two given data values as our points 1 and 2 respectively. And that is what we are going to use to create a linear function for pressure

Let the y and x represent the pressure and depth respectively

point 1 (30, 4) and point 2 (50, 6)

slope(m) = y2-y1 / x2-x1

where  x1 =30, y1 = 4 and x2 = 50, y2 = 6

slope(m) = 6-4 / 50-30 = 2/20 = 1/10

Linear function are of the form y-y1 = m(x-x1). Thus:

y-4 = 1/10 (x-30)

y-4 = 1/10(x) - 3

y = 1/10(x) + 1 = 0.1x + 1

Therefore, the linear function for pressure based on the depth in meters is y = 0.1x + 1

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The original amount of nuts, x, in the recipe is 103

The equation for the original amount is 2x + 2x = 412

An algebraic expression can be defined as an expression made up of terms, factors, constants, coefficients, and variables.

These expressions are also known to be made up of mathematical operations such as;

From the information given, we have that;

Beverly doubles the amount of nuts and peanut butter chips

Total number = 412

This is represented as;

2x + 2x = 412

collect like terms

4x = 412

Make 'x' the subject of formula

x = 412/ 4

x = 103

Hence, the value is 103

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Answer:

-3

Step-by-step explanation:

You can use  to find the slope of a line going through  and .

I like to line up the points and subtract vertically. Then put 2nd difference over 1st difference.

(6,h)

minus

(7,-10)

------------

-1     h-(-10)

This also said to be equal to -7:

Multiply -1 on both sides:

Subtract 10 on both sides:

[texh=-3[/tex]

So if h=-3 then the slope of the line going through (6,h) and (7,-10) is -7.

Let's test it:

(6,-3)

minus

(7,-10)

----------

-1  7

So the slope is 7/-1=-7. This is the intended goal.

The check is good.

Answer:

I believe it's 4.5 seconds

The equation of the line perpendicular to y = - (1 / 2) · x - 2 and that passes through the point (x, y) = (- 3, - 5) is y = 2 · x + 1.

In this problem we must determine the equation of a line perpendicular to another line, provided that the equation of a line and a point of intersection are given. According to analytical geometry, two lines are perpendicular if and only if the product of the two slopes equals - 1.

The equations of the line are defined by functions of the form:

y = m · x + b

Where:

And the slope relationship between two perpendicular line:

m · m' = - 1

Where:

First, derive the equation of the line in slope-intercept form:

x + 2 · y = - 4

2 · y = - x - 4

y = - (1 / 2) · x - 2

Second, calculate the slope of the perpendicular line by the slope relationship:

m' = - 1 / (- 1 / 2)

m' = 2

Third, find the y-intercept of the perpendicular line by the equation of line, the slope and the coordinates of the given point:

b = y - m · x

b = - 5 - 2 · (- 3)

b = - 5 + 6

b = 1

Then, obtain the equation of the line in slope-intercept form:

y = 2 · x + 1

The equation of the line is y = 2 · x + 1.

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Tower B is 14.9 miles away from the fire.

What is the law of sines?

According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.

Here,

According to the law of sines

BC/sin A = AC/sin B = AB/sin C

∠A = 43°, ∠B = 31°, ∠C = 180° - ∠A - ∠B = 106°

AB = 21 miles

So, BC = (AB/SinC)×SinA

BC = 14.9 miles

Hence, Tower B is 14.9 miles away from the fire.

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Answer:

After 8 minutes ; altitude = 22,400 feet

Step-by-step explanation:

s1 = 2800t

s2 = -3200t + 48 000

2800t = -3200t + 48 000

28t = -32t + 480

7t = -8t + 120

7t + 8t = 120

15t = 120

15/15 t = 120/15

t = 8 minutes

s = 8 * (2800)  =   22400 feet

Answer:

y = m x + b       equation for a straight line

when x = 4     y = 5

5 = m * 4 + b

m = (5 - b) / 4      solving for m

when x = -3      y = -1

-1 = (5 - b) / 4 * -3 + b = -3 * (5 - b) / 4 + 4 b / 4

-1 = (-15 + 3 b + 4 b) / 4

11 = 7 b      b = 11 / 7

Since m = (5 - b) / 4

m = (5 - 11/7) / 4  = 6/7

We then have y = 6 x / 7 + 11 / 7

Or 7 y = 6 x + 11

Check:

when (4 , 5)     35 = 24 + 11 = 35

The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10)  (18, 7) (17, 8), and (16, 9).

A square number, also known as a perfect square, is an integer that is the square root of another integer, or the result of multiplying another integer by itself.

For example:

Square of 2 = 4

Square of 3 = 9

Square of 4 = 16

Here we have  

A science class is pretty small

There are just 18 students in the class.

The teacher gave each of them numbers from 1 through 18 on lab days

Start from 1 and find by adding which number we will get a square number

Here  1 + 15 = 16

2 + 14 = 16

3 + 13 = 16

4 + 12 = 16

5 + 11 = 16

6 + 10 =16

After the above combinations, the remaining numbers are

7, 8, 9, 16, 17, 18          

which can be added as given below to get square number 25  

=>  18+7=25

=>  17+8=25

=>  16+9=25  

Therefore,

The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10)  (18, 7) (17, 8), and (16, 9)  

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Answer:

I think is 50m.

Step-by-step explanation:

The common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.

a.

common ratio r = a2/a1

= -3360/4480

= -0.75.

r = a3/a2

= 2520/-3360

= -0.75

b.

[tex]a_{n}[/tex] = a*r^(n-1)

here a = 4480 and r = -0.75.

= 4480(-0.75)^(20-1)

= 4480(-0.75)^19

= 4480*(-0.00422)

[tex]a_{20}[/tex] = -18.9056.

c.

[tex]s_{n}[/tex] = a*((1-r^n)/(1-r))

= 4480*((1--0.75^4)/(1--0.75))

= 4480*((1-0.31640625)/(1--0.75))

= 4480*(0.68359375/1.75)

= 4480*0.390625

= 1750

Therefore the common ratio, r = -0.75, 20th term = -18.9056, exact sum of the infinite sequence = 1750.

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Answer:b=2/3 if u don't need an answer that is not a fraction or decimal u can write 17. as a whole number.

Step-by-step explanation:

Answer: 17 Dimes.

Step-by-step explanation:

Answer:

X = 2, Y = 0

Step-by-step explanation:

Add the two equations together to cancel out -4y and +4y

leaving you with:

8x = 16

8x = 16

divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)

leaving you with:

x = 2

substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):

8(2) - 4 y = 16

8 x 2 = 16

leaving you with:

16 - 4y = 16

subtract 16 from both sides to get 4y on its own

leaving you with:

-4y = 0

so y = 0, and x = 2

We can conclude that train A is moving faster than train B

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

The distance y (in miles) that train A travels in [x] amount of time is represented by the equality y = 78x. The graph shows the distance that train B travels.

Train A is moving with speed s[A] = 78 miles/hour {As slope of the equation is 78}. The train B will move with speed given by -

s[B] = (132 - 66)/(2 - 1) = 66 miles/hour

Therefore, we can conclude that train A is moving faster than train B

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[In the complete question it is asking to find which train is moving faster]

Answer:

A)- 65

B)- 25

c)- 25

To find A- pay attention to the bottom..add 60+55 then subtract that from 180

yu get 65..now we know that 65+90= 155 subtract that from 180 you get 25. so now we have B..B and C are congruent meaning they are equals

hope this helps

Using the concepts of probability, we got that 0.4286 is the probability  that the battery life for an iPad Mini will be 10 hours or less  which is about 42.86%.

From the given information;

Let  X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

[tex]f_X(x)[/tex] = [tex]\frac{1}{B-A}[/tex] where A<x<B

where A and B  are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

[tex]f_X(x)[/tex] = [1 / (12-8.5)]8.5<x<12

[tex]f_X(x)=[/tex](1/3.5)8.5<x<12

The  probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

F(10)=[tex](x-A)/(B-A)[/tex]

F(10)=(10-8.5)/(12-8.5)

F(10)=1.5/3.5

F(10)=0.4286

Hence, the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286

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(Complete question)

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

Answer:

x = 9/5 y - 4/5

Step-by-step explanation:

Make x the subject:

9y - 5x =4

Subtract 9y from each side

9y-9y - 5x =-9y+4

-5x = -9y +4

Divide each side by -5

-5x/-5 = -9y/-5 + 4/-5

x = 9/5 y - 4/5

Answer:

x = (9/5)y - (4/5)

Step-by-step explanation:

Given equation,

→ 9y - 5x = 4

Solving for the required value of x,

→ 9y - 5x = 4

→ -5x = -9y + 4

→ x = (-9y + 4)/-5

→ [ x = (9/5)y - (4/5) ]

Hence, value of x = (9/5)y - (4/5).

Yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.

What is t statistic and critical value of t?

T statistic is ratio of a parameter's estimated value to its standard error when it deviates from its hypothesized value.

Critical t value is a cut-off point in t distribution

In question, the calculated t statistic is 8.1023 and critical t value one tail is 1.7139 and critical t value two tail is 2.0686. So, the value of calculated t statistic is higher than critical t value one tail or two tail. Therefore, we can reject the null hypothesis.

Thus, yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.

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The probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.

We have following information,

the demand for the polymer is distributed normally .

Mean (μ) = 250 gallons and Standard deviations (σ) = 125 gallons

Selling price of poymer = $25 per gallons

cost price of raw material for polymer= $ 10 per gallons

Salvage value = $(-5)/ gallon

Now, Using the formula for normally distributed sample,

Z = ( X - μ ) /σ

where , X---> sample mean

μ ----> population mean

σ----> standard deviations

Z -----> Z-value

from question it is clear X = 150

putting all the values of variables in above formula we get, Z = ( 150-250)/125 = -100/125

= - 0.8

(-0.8) value of z = 0.21 = 21% , the value of z is measure from normal distribution table.

They will run out of raw material if demands exceds this quantity or

Probability ( out of stock ) = 1 - 0.21 = 0.79 = 79%

So, the probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.

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#Complete Question :

Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop's purchases raw material for $10 per gallon and Goop mrust spend $5 per gallon to dispose off all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) That is to say, the salvage value is $(-5)/gallon. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost. ?

1. Suppose Good purchases 150 gallons of raw material. What is the probability that they will run out of raw material? ?

Answer:

g(10)=-33, x=3

Step-by-step explanation:

g(x)=-4x+7. --------(1)

a) g(10)=?

since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x

g(10)=-4(10)+7

g(10)=-40+7

g(10)= -33

b.)find x if g(x)=-5. ---------(ii)

g(x)=-4x+7. we will place (I) in (ii)

g(x)=-5

-4x+7=-5

-4x=-5-7

-4x=-12

cancel the minus(-) sign in both sides

4x=12

x=12/4

x=3

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The length of the shortest ladder is 16.64 ft.

In triangle ABC, using Pythagoras theorem

[tex]AC^{2} = AB^{2} + BC^{2}[/tex]  OR

[tex]L^{2} = h^{2} + (x+4)^{2}[/tex]       .....(1)

We also have similar triangles if we consider:

△ABC and △DEC

Which gives us the proportional relationship:

AB:DE = BC:EC

or    h/8 = (4+x) / x

h = 8( 4+x) /x      

Substituting this last expression for h into Eq [1] we get:

[tex]L^{2} = \frac{(8(x+4))^{2} }{x^{2} } + (x+4)^{2}[/tex]

Our aim is to now minimize L wrt x, and this involves looking for critical points of the derivative, so differentiation wrt x we get:

[tex]2L\frac{dL}{dx} = 2( 8 + \frac{32}{x} ) (-\frac{32}{x^{2} } ) + 2(x+4)[/tex]

At a critical point the derivative is zero and so we have the equation:

         =  [tex]2 (x + 4) ( 1 - \frac{256}{x^{3} } ) = 0[/tex]

From here we can find the value x :

x + 4 = 0                                                            1 - [tex]\frac{256}{x^{3} }[/tex]  = 0

x = -4                                                                 x  = [tex]\sqrt[3]{256}[/tex]

We require x > 0 so we neglect the -ve solution and only take +ve solution

therefore the minimum height of the ladder can be given by putting the value of x in eqn 1.

[tex]L^{2} = ( 8 + \frac{32}{\sqrt[3]{256} } )^{2} + ( \sqrt[3]{256} +4) ^{2}[/tex]

L² = 277.14

L = 16.64 ft

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The slope of the line is 0.393.

Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").

Given,

A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.

We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:

m = 8ₓ/8ₐ

where m is the slope of the best-fit line.

8ₓ = Standard deviation of the x-coordinates is 5.591,

8ₐ =  the standard deviation of the y-coordinates is 2.772.

Slope is:

m = 8ₐ/8ₓ

m = (0.793)(2.772)/5.591

m = 0.393

The slope of the line is 0.393.

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Nick got a total of $33.25 for his part of work.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked.

Assume that Nick recieved $[x]. Then, Pam will get - (52.25 - x). For direct proportionality -

y₁/x₁ = y₂/x₂

We can write -

x/3.5 = (52.25 - x)/2

2x = 3.5(52.25 - x)

2x = 182.875 - 3.5x

x = 33.25

Therefore, Nick got a total of $33.25 for his part of work.

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The solution set for the inequality is.

-113 ≤ y ≤ 131

Here we have the following inequality:

|y - 9| ≤ 122

Any absolute value inequality can just be decomposed as follows:

|y - 9| ≤ 122

to:

-122 ≤  y - 9 ≤  122

Now we can solve this for y by adding 9 in all places:

-122 + 9 ≤ y - 9 + 9 ≤  122 + 9

-113 ≤ y ≤ 131

That is the solution set.

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